
\emph{Global} formulae relate several hidden ground atoms. We use them for two 
purposes: to ensure consistency between the decisions of all SRL stages and to 
capture some of our intuition about the task. We will refer to formulae that 
serve the first purpose as \emph{structural constraints}. For example, a 
structural constraint is given by the (deterministic) formula
\[\role(p,a,r) \Rightarrow \hasRole(p,a)\]
which ensures that, whenever the argument $a$ is given a label $r$ with respect 
to the predicate $p$, this argument must be an argument of $a$ as denoted by 
\emph{hasRole(p,a)}.

The global formulae that capture our intuition about the task itself can be 
further divided into two classes. The first one uses deterministic or 
\emph{hard} constraints such as
\begin{eqnarray*}
       & \role(p,a,r_1) \wedge r_1 \neq r_2 \Rightarrow \neg \role(p,a,r_2)\\
\end{eqnarray*}
which forbids cases where distinct arguments of a predicate have the same role 
unless the role describes a modifier.

The second class of global formulae is \emph{soft} or nondeterministic. For 
instance, the formula
\begin{eqnarray*}
  & \lemma(p,+l) \wedge \ppos(a,+p)  \\
  & \wedge \hasRole(p,a)  \Rightarrow \sense(p,+f)
  \end{eqnarray*}
is a soft global formula. It captures the observation that the sense of a verb 
or noun depends on the type of its arguments. Here the type of an argument token 
is represented by its POS tag.

Table \ref{tbl:global} presents the global formulae used in this model. 

\begin{table}[ht]
    \centering
    \small
    \begin{tabular}{|p{7.0cm}|}\hline
        \multicolumn{1}{|c|}{Structural constraints}\\\hline
       $\hasRole(p,a) \Rightarrow \isArgument(a)$\\
       $\role(p,a,r) \Rightarrow \hasRole(p,a)$\\\hline
       $\isArgument(a)  \Rightarrow\exists p.\hasRole(p,a)$\\
       $\hasRole(p,a) \Rightarrow\exists r. \role(p,a,r)$\\\hline
       \multicolumn{1}{|c|}{Hard constraints}\\\hline
       $\role(p,a,r_1) \wedge r_1 \neq r_2 \Rightarrow \neg \role(p,a,r_2)$\\
       $\sense(p,s_1) \wedge s_1 \neq s_2 \Rightarrow \neg \sense(p,r_2) $\\
       $\role\left(p,a_{1},r\right)\wedge \neg mod\left(r\right)\wedge a_{1}\neq 
       a_{2}  \Rightarrow \neg role\left(p,a_{2},r\right) $ \\\hline
       \multicolumn{1}{|c|}{Soft constraints}\\\hline
       $\role\left(p,a_{1},r\right)\wedge \neg mod\left(r\right)\wedge a_{1}\neq 
       a_{2}  \Rightarrow \neg role\left(p,a_{2},r\right) $ \\
       $ \plemma(p,+l) \wedge \ppos(a,+p) \wedge \hasRole(p,a)  \Rightarrow 
       sense(p,+f) $ \\
       $ \plemma(p,+l) \wedge \role(p,a,+r) \Rightarrow \sense(p,+f) $ \\
        \hline
    \end{tabular}
    \caption{Global formulae for ML model}
    \label{tbl:global}
\end{table}

